Modify the recursive tree program using one or all of the following
ideas:

Modify the thickness of the branches so that as the branchLen
gets smaller, the line gets thinner.

Modify the color of the branches so that as the branchLen gets
very short it is colored like a leaf.

Modify the angle used in turning the turtle so that at each branch
point the angle is selected at random in some range. For example
choose the angle between 15 and 45 degrees. Play around to see
what looks good.

Modify the branchLen recursively so that instead of always
subtracting the same amount you subtract a random amount in some
range.

If you implement all of the above ideas you will have a very
realistic looking tree.

Find or invent an algorithm for drawing a fractal mountain. Hint: One
approach to this uses triangles again.

Write a recursive function to compute the Fibonacci sequence. How
does the performance of the recursive function compare to that of an
iterative version?

Implement a solution to the Tower of Hanoi using three stacks to keep
track of the disks.

Using the turtle graphics module, write a recursive program to
display a Hilbert curve.

Using the turtle graphics module, write a recursive program to
display a Koch snowflake.

Write a program to solve the following problem: You have two jugs: a
4-gallon jug and a 3-gallon jug. Neither of the jugs have markings on
them. There is a pump that can be used to fill the jugs with water.
How can you get exactly two gallons of water in the 4-gallon jug?

Generalize the problem above so that the parameters to your solution
include the sizes of each jug and the final amount of water to be
left in the larger jug.

Write a program that solves the following problem: Three missionaries
and three cannibals come to a river and find a boat that holds two
people. Everyone must get across the river to continue on the
journey. However, if the cannibals ever outnumber the missionaries on
either bank, the missionaries will be eaten. Find a series of
crossings that will get everyone safely to the other side of the
river.

Modify the Tower of Hanoi program using turtle graphics to animate
the movement of the disks. Hint: You can make multiple turtles and
have them shaped like rectangles.

Pascal’s triangle is a number triangle with numbers arranged in
staggered rows such that

\[a_{nr} = {n! \over{r! (n-r)!}}\]

This equation is the equation for a binomial coefficient. You can
build Pascal’s triangle by adding the two numbers that are diagonally
above a number in the triangle. An example of Pascal’s triangle is
shown below.

111121133114641

Write a program that prints out Pascal’s triangle. Your program
should accept a parameter that tells how many rows of the triangle to
print.